We use a standard trick (see e.g., [1]}): We first reduce \(\textsc {2D-GD-FixedPoint}\)  to the problem of finding a well supported \(\epsilon ^{\prime }_N\) -Nash equilibrium. Thereafter, we can use the fact that the problem of finding a well-supported \(\epsilon ^{\prime }_N\) -Nash equilibrium can be reduced to the problems of finding \(\epsilon _N\) -Nash equilibrium; see [1]}. For clarity of presentation, in this section and in Section REF  we argue about exact equilibria. However, all our arguments remain valid also for the case of well-supported \(\epsilon ^{\prime }_N\) -Nash equilibrium for \(\epsilon ^{\prime }_N\ll \epsilon _T^2\) .
